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Sunyoung Kim (skimewha.ac.kr) Abstract: Sequences of generalized Lagrangian duals and their SOS (sums of squares of polynomials) relaxations for a POP (polynomial optimization problem) are introduced. Sparsity of polynomials in the POP is used to reduce the sizes of the Lagrangian duals and their SOS relaxations. It is proved that the optimal values of the Lagrangian duals in the sequence converge to the optimal value of the POP using a method from the penalty function approaches. The sequence of SOS relaxations is transformed into a sequence of SDP (semidefinite program) relaxations of the POP, which correspond to duals of modification and generalization of SDP relaxations given by Lasserre for the POP. Keywords: Polynomial Optimization Problem, Sparsity, Global Optimization, Lagrangian Relaxation, Lagrangian Dual, Sums of Squares Optimization, Semidefinite Program, Semidefinite Program Relaxation Category 1: Global Optimization (Theory ) Category 2: Linear, Cone and Semidefinite Programming (Semidefinite Programming ) Citation: Research Report B395, Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, Japan, Sept./2003 Download: [Postscript][PDF] Entry Submitted: 09/29/2003 Modify/Update this entry  
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